Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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BI-LIPSCHITZ PROPERTY AND DISTORTION THEOREMS FOR PLANAR HARMONIC MAPPINGS WITH M-LINEARLY CONNECTED HOLOMORPHIC PART

  • Huang, Jie (School of Mathematical Sciences Huaqiao University) ;
  • Zhu, Jian-Feng (School of Mathematical Sciences Huaqiao University)
  • Received : 2017.09.23
  • Accepted : 2018.01.29
  • Published : 2018.09.30
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Abstract

Let $f=h+{\bar{g}}$ be a harmonic mapping of the unit disk ${\mathbb{D}}$ with the holomorphic part h satisfying that h is injective and $h({\mathbb{D}})$ is an M-linearly connected domain. In this paper, we obtain the sufficient and necessary conditions for f to be bi-Lipschitz, which is in particular, quasiconformal. Moreover, some distortion theorems are also obtained.

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References

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